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Mn$_{3}$X (X= Sn, Ge) are noncollinear antiferromagnets hosting a largeanomalous Hall effect (AHE). Weyl nodes in the electronic dispersions arebelieved to cause this AHE, but their locus in the momentum space is yet to bepinned down. We present a detailed study of the Hall conductivity tensor andmagnetization in Mn$_{3}$Sn crystals and find that in the presence of amoderate magnetic field, spin texture sets the orientation of the $k$-spaceBerry curvature with no detectable in-plane anisotropy due to the $Z_6$symmetry of the underlying lattice. We quantify the energy cost of domainnucleation and show that the multidomain regime is restricted to a narrow fieldwindow. Comparing the field dependence of AHE and magnetization, we find thatthere is a distinct component in the AHE which does not scale withmagnetization when the domain walls are erected. This so-called `topological'Hall effect provides indirect evidence for a non-coplanar spin components andreal-space Berry curvature in domain walls.

Momentum-space and real-space Berry curvatures in Mn$_{3}$Sn